From Phase Space Representation to Amplitude Equations in a Pattern Forming Experiment

Abstract

We describe and demonstrate a method to reconstruct an amplitude equation from the nonlinear relaxation dynamics in the succession of the Rosensweig instability. A flat layer of a ferrofluid is cooled such that the liquid has a relatively high viscosity. Consequently, the dynamics of the formation of the Rosensweig pattern becomes very slow. By sudden switching of the magnetic induction, the system is pushed to an arbitrary point in the phase space spanned by the pattern amplitude and the magnetic induction. Afterwards, it is allowed to relax to its equilibrium point. From the dynamics of this relaxation, we reconstruct the underlying fully nonlinear equation of motion of the pattern amplitude. The measured nonlinear dynamics serves to select the best weakly nonlinear expansion which describes this hysteretic transition.

20 pages, 12 figures

References in corpus (8)

• Two-dimensional solitons on the surface of magnetic fluids
• The Surface Topography of a Magnetic Fluid -- a Quantitative Comparison between Experiment and Numerical Simulation
• Pattern and wavenumber selection in ferrofluids
• Growth of surface undulations at the Rosensweig instability
• Hexagons become second if symmetry is broken
• Scaling Behaviour of the Maximal Growth Rate in the Rosensweig Instability
• The normal field instability under side-wall effects: comparison of experiments and computations
• The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids

Cited by in corpus (3)

• Systematic experimental exploration of bifurcations with non-invasive control
• Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation
• Retarding the growth of the {Rosensweig} instability unveils a new scaling regime